Current integration force and displacement self-sensing method for cantilevered piezoelectric actuators

This paper presents a new method of self-sensing both of the displacement and the external applied force at the tip of piezoelectric cantilevers. Integrated electric current across piezoelectric actuators is compensated against material nonlinearities (creep, hysteresis) to provide reliable information. We propose to compensate the hysteresis by using the Prandtl–Ishlinskii static approach while an auto regressive and moving average exogenous (ARMAX) model is used to minimize the creep influence. The quasistatic estimation, electronic circuit, and aspects related to long-term charge preservations are described or referenced. As an experiment, we tested the actuator entering in contact with a fixed force sensor. An input signal of 20 V peak-to-peak (10% of maximum range) led to force self-sensing errors inferior to ±8%. A final discussion about method accuracy and its limitations is made.